基于应变梯度中厚板单元的石墨烯振动研究

徐巍; 王立峰; 蒋经农

doi:10.6052/0459-1879-15-074

基于应变梯度中厚板单元的石墨烯振动研究

徐巍^1,2,
王立峰^1, ,,
蒋经农¹

1.
南京航空航天大学, 机械结构力学及控制国家重点实验室, 南京210016
2. 中国航空动力机械研究所, 株洲412002

基金项目: 教育部新世纪优秀人才支持计划(NCET-11-0832),江苏省第四期"333工程"培养资金资助项目以及中央高校基本科研业务费专项资金.

详细信息

通讯作者:
王立峰,教授,主要研究方向:纳尺度结构动力学.E-mail:walfe@nuaa.edu.cn

中图分类号: O326
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出版历程
- 收稿日期: 2015-03-04
- 修回日期: 2015-06-28
- 刊出日期: 2015-09-17

FINITE ELEMENT ANALYSIS OF STRAIN GRADIENT MIDDLE THICK PLATE MODEL ON THE VIBRATION OF GRAPHENE SHEETS

1.
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2. China Aviation Powerplant Research Institute, Zhuzhou 412002, China

Funds: The project was supported by the Program for New Century Excellent Talents in University (NCET-11-0832), 333 Talents Program in Jiangsu Province and Fundamental Research Funds for the Central Universities of China.

摘要

摘要: 基于应变梯度理论建立了单层石墨烯等效明德林(Mindlin) 板动力学方程,推导了四边简支明德林中厚板自由振动固有频率的解析解. 提出了一种考虑应变梯度的4 节点36 自由度明德林板单元,利用虚功原理建立了单层石墨烯的等效非局部板有限元模型. 通过对石墨烯振动问题的研究,验证了应变梯度有限元计算结果的收敛性. 运用该有限元法研究了尺寸、振动模态阶数以及非局部参数对石墨烯振动特性的影响. 研究表明,这种单元能够较好地适用于研究考虑复杂边界条件石墨烯的尺度效应问题. 基于应变梯度理论的明德林板所获得石墨烯的固有频率小于基于经典明德林板理论得到的结果. 尺寸较小、模态阶数较高的石墨烯振动尺度效应更加明显. 无论采用应变梯度理论还是经典弹性本构关系,考虑一阶剪切变形的明德林板模型预测的固有频率低于基尔霍夫(Kirchho) 板所预测的固有频率.
- 应变梯度 /
- 有限元 /
- 明德林板 /
- 振动 /
- 尺度效应
Abstract: The dynamics equation of the Mindlin middle thick plate model based on strain gradient theory is formulated to study the vibration of single-layered graphene sheets (SLGSs). Analytical solution of the natural frequency for free vibration of Mindlin plate with all edges simply-supported is derived. A 4-node 36-degree-of-freedom (DOF) Mindlin plate element is proposed to build the nonlocal finite element (FE) plate model with second order gradient of strain taken into consideration. This FE method is used to study the influences of the size, vibration mode and nonlocal parameters on the scale effect of vibration behaviors of SLGSs, which validates the reliability of the FE model for predicting the scale effect on the vibrational SLGSs with complex boundary conditions. The natural frequencies obtained by the strain gradient Mindlin plate are lower than that obtained by classical Mindlin plate model. The natural frequencies of SLGSs obtained by Mindlin plate model with first-order shear deformation taken into account are lower than that obtained by Kirchhoff plate model for both strain gradient model and classical case. The small scale effect increases with the increase of the mode order and the decrease of the size of SLGSs.
- strain gradient /
- finite element method /
- Mindlin plate /
- vibration /
- scale e ect

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